This invention relates to an apparatus that uses a plurality of one-dimensional, axisymmetric or two-dimensional lenses for the focusing, collection, imaging, and general manipulation of neutrons for medical, industrial and scientific applications.
Backgroundxe2x80x94Compound Refractive Lenses for X-rays
In the literature the collection and focusing of x-rays and neutrons has been accomplished using multiple refractive lenses composed of cylindrical, spherical and parabolic lenses. It has long been known for optics in the visible spectrum that a series of N closely spaced lenses, each having a focal length of f1, has an overall focal length of f1/N (e.g. F. L. Pedrotti and L. Pedrotti, xe2x80x9cIntroduction to Optics,xe2x80x9d Prentice Hall, Chapt. 3. p.60, 1987).
Also in the literature Toshihisa Tomie (U.S. Pat. No., 5,594,773) and A. Snigirev, V. Kohn, I. Snigireva and B. Lengeler, (xe2x80x9cA compound refractive lens for focusing high-energy X-rays, Nature 384, 49 (1996)) have shown that this can also be done in the x-ray region of the spectrum using a series of holes drilled in a common substrate that effectively mimics a linear series of lenses. This xe2x80x9ccompound refractive x-ray lensxe2x80x9d (CRL) is manufactured using N number of unit lenses, each constituted by a series of hollow cylinders or holes that are embedded inside a material capable of transmitting x-rays. Two closely spaced holes form a concave-concave (bi-concave) lens at their closest juncture. N holes result in N unit lenses. For x rays as well as for neutrons, the index of refraction of the material is less than 1; thus, unlike visible light refraction optics, which will cause visible rays to diverge, the bi-concave lens performs in opposite fashion and focuses x-rays and neutrons instead.
Individual Unit Lenses for X-rays
M. A. Piestrup, J. T. Cremer, R. H. Pantell and H. R. Beguiristain (U.S. Pat. No. 6,269,145) have used an array of individual thin lenses without a common substrate but with a common optical axis to form a refractive x-ray lens. These individual unit lenses can be parabolic, spherical, cylindrical or Fresnel. The patent shows that small random displacements of the individual lenses off a common axis will not invariably lead to the lens array failure to collect and focus x-rays. It shows that the prior teachings of Tomie are incorrect concerning the difficulty of achieving collection and focusing from a linear series of individually separate refractive lenses which are slightly displaced from one another. Small random displacement off the average axis of a linear series of lens elements which form a compound refractive lens are shown by Piestrup et al. (U.S. Pat. No. 6,269,145) not to dramatically affect the focal spot size, focal length of the lens, and the lens aperture size. Separate thin lenses are possible since the lenses need not be exactly in contact. This allows the unit lenses to be individually supported by structures that are thicker than the thin lenses, such as a rigid-ring structure. The unit lenses are then separated by a gap that is equal to that of the thickness of the support structure. The addition of the gap does not affect the collection and focusing of the x-rays as long as we can assume the thin lens formula assumption is still correct (f greater than  greater than l), where l is the length of the CRL including the gaps between the unit lenses and f is the focal length of the CRL. The lens will still work if the CRL is thick (f≈l), but the simple formula for the focal length must be modified.
In the literature a closely-spaced series of N bi-concave lenses each of focal length f1 results in a focal length f of:                     f        =                                            f              1                        N                    =                                    R                              2                ⁢                N                ⁢                                  xe2x80x83                                ⁢                δ                                      .                                              (        1        )            
The unit lens focal length f1 is given by:                                           f            1                    =                      R                          2              ⁢                              xe2x80x83                            ⁢              δ                                      ,                            (        2        )            
where the complex refractive index of the unit lens material is expressed by:                               n          =                      1            -            δ            +                                          i                ⁡                                  (                                      λ                                          4                      ⁢                      π                                                        )                                            ⁢              μ                                      ,                            (        3        )            
R is the radius of curvature of the lens, xcex is the neutron wavelength and xcexc is the linear attenuation coefficient of in the lens material. For cylindrical lenses R=Rh, the radius of the cylinder, for spherical lenses R=Rs, the radius of the sphere; for the case of parabolic unit lenses R=Rp, the radius of curvature at the vertex of the paraboloid.
The aperture of the lens array is limited. This is due to increased absorption at the edges of the lens as the lens shape may be approximated by a paraboloid of revolution that increases thickness in relation to the square of the distance from the lens axis. These effects make the compound refractive lens act like an iris as well as a lens. For a radius R =Rh, Rs, or Rp, the absorption aperture radius ra is given by Tomie and Snigirev et al. to be:                               r          a                =                                            (                                                2                  ⁢                  R                                                  μ                  ⁢                                      xe2x80x83                                    ⁢                  N                                            )                                      1              2                                =                                                    (                                                      4                    ⁢                                          xe2x80x83                                        ⁢                    δ                    ⁢                                          xe2x80x83                                        ⁢                    f                                    μ                                )                                            1                2                                      .                                              (        4        )            
If the lenses refract with spherical surfaces, only the central region of the lens approximates the required paraboloid of revolution shape of an ideal lens. The parabolic aperture radius rp where there is a xcfx80 phase change from the phase of an ideal paraboloid of revolution given by:                               r          p                =                              2            ⁢                                          (                                                                            (                                              Nf                        ⁢                                                  xe2x80x83                                                ⁢                        δ                                            )                                        2                                    ⁢                  λ                  ⁢                                      xe2x80x83                                    ⁢                                      r                    i                                                  )                                            1                4                                              ≈                      2            ⁢                                          (                                                                            (                                              N                        ⁢                                                  xe2x80x83                                                ⁢                        δ                                            )                                        2                                    ⁢                                      f                    3                                    ⁢                  λ                                )                                            1                4                                                                        (        5        )            
where ri is the image distance and xcex is the X-ray wavelength. Rays outside this aperture do not focus at the same point as those inside. The approximation in (5) is true for a source placed at a distance much bigger than f. For imaging the effective aperture radius re is the minimum of the absorption aperture radius, ra, and the parabolic aperture radius, rp, and the mechanical aperture radius rh=Rh; that is:
re=MIN(ra, rp, rh).xe2x80x83xe2x80x83(6)
As shown by Piestrup et al, the compound refractive lens made of spherical, parabolic and cylindrical unit lenses can tolerate a small random displacement of the individual lens elements off the average axis. This is shown in FIG. 1 wherein unit bi-concave lenses 9 are aligned as carefully as possible, but, due to unavoidable error, each has a displacement of ti off the mean optical axis 8 of all the unit lenses. In order to keep an adequate aperture, the root mean square, "sgr"t, of the average displacement of the unit lenses off the average optical axis of the unit lenses should be less than the effective aperture radius of the individual lenses or:
"sgr"t less than rexe2x80x83xe2x80x83(7)
As shown by Piestrup et al. (U.S. Pat. No. 6,269,145), the aperture is reduced somewhat when there is random variation of the unit lenses off the average optical axis of the lenses.
Piestrup et al (U.S. Pat. No. 6,269,145) also showed that if a refractive Fresnel lens is utilized for x-rays, absorption can be minimized and a large aperture can be achieved. Indeed, the aperture radius of the lens can be the mechanical aperture radius, rm. However, because there must be phase addition of the x-rays between each Fresnel zone, the standard deviation of each unit Fresnel lens must not be larger than the width of the smallest zone that is smxe2x88x92smxe2x88x921. Piestrup et al. (U.S. Pat. No. 6,269,145) shows that the requirement is "sgr"txe2x89xa6(smxe2x88x92smxe2x88x921)/4. This is a more stringent requirement than the ordinary spherical, parabolic or cylindrical lenses. To cover most applications for x-rays where the Fresnel lens would still practically work with minor loss, Piestrup et al. (U.S. Pat. No. 6,269,145) required that "sgr"txe2x89xa6(smxe2x88x92smxe2x88x921.
Backgroundxe2x80x94Compound Refractive Lenses for Neutrons
R. Gxc3xa4hler, J. Kalus, and W. Mampe (Phys. Rev. D 25, 2887, 1982) use a neutron compound lens system (two unit lenses) to measure the electric charge of neutrons. This same setup is used as a practical example of lenses in neutron optics by Varley F. Sears, (Neutron Optics, Ch. 3, p 73-74, Oxford University Press, 1989). This reference clearly states that the compound refractive lens focal length f of the system of two unit lenses each of focal length fi is reduced by the number of unit lenses of the compound system i.e. f=fi/2.
It is known in the art that the collection and focusing of neutrons can be accomplished using multiple refractive lenses composed of cylinders, spherical and parabolic lenses. D. J. Bishop et al. (U.S. Pat. No., 5,880,478) have shown that focusing of neutrons can be done using a series of unit lenses. No mention of the importance of the alignment of these lenses is given. This issue of the effect of small random displacements of the individual lenses off a common axis on the collection and focusing of neutrons is not discussed for these simple double concave lenses. As in Piestrup et al, U.S. Pat. No. 6,269,145, these lenses can be separate, without a common substrate. These lenses are concave and either spherical or parabolic in shape.
Backgroundxe2x80x94Neutron Microscope
In the art there is a class of microscopes that uses neutron mirrors with ultra-cold neutrons, wavelengths around 396 xc3x85, and very cold neutrons, wavelengths around 40 xc3x85 to image samples from reflections on neutron mirror curved surfaces as described by A. I Frank in the Proceedings of the SPIE v1738, 1992, Bellingham, Wash., USA p323-334.
Backgroundxe2x80x94Achromatic X-ray Compound Refractive Lenses
In the literature of M. A. Piestrup, J. T. Cremer, R. H. Pantell and H. R. Beguiristain (U.S. Pat. No. 6,269,145), x-ray compound refractive lenses are capable of having close to identical focal length over large variations in x-ray photon energy. This is achieved by placing the lenses an appropriate distance, d, apart. Achromatic neutron lens arrays can be constructed in the same fashion analogous to x-ray compound refractive lenses.
Backgroundxe2x80x94Neutron Monochromator
Currently, the most favored methods for monochromatizing neutron beams are mechanical methods and neutron reflection and diffraction from multilayer mirrors, multi-channel xe2x80x9clensesxe2x80x9d, and most notably Bragg reflection-diffraction from crystals.
a. Mechanical Neutron Monochromator
It is known in the art to use mechanical methods that take advantage of the kinetic energy of the neutrons for filtering them. One example of a mechanical monochromator was demonstrated by S. M. Kalebin, G. V. Rukolaine, A. N. Polozov, V. S. Artamonov, R. N. Ivanov and V. S. Chemishov, (xe2x80x9cNeutron monochromator with five synchronously rotating rotors suspended in a magnetic field,xe2x80x9d Nucl. Inst. Meth. Phys. Res., Sect. A vol. 267 pp. 35-40) has five neutron choppers consisting of rotary discs having apertures for pulsing, or chopping, a neutron beam. It produces short pulses at high repetition rates of high intensity monochromatic neutrons. Such devices are expensive to construct and maintain and are limited with respect to changing pulse duration and rate for a given neutron wavelength.
b. Neutron Monochromators that use Reflections and Diffraction From Different Surfaces
Earlier methods include the pulsed-neutron monochromator described by Herbert A. Mook (U.S. Pat. No. 4,543,230) where a row of crystals that reflect neutrons intercepts a beam of neutrons and reflect onto a common target. The crystals in the row define progressively larger neutron-scattering angles and are vibrated sequentially in descending order with respect to the size of their scattering angles, thus generating neutron pulses that arrive simultaneously at the target. Other monochromators are also known that use nearly perfect single crystals of silicon, silicon dioxide, quartz and the like which could be bent. In some monochromators, a row of crystals is disposed in a neutron beam, with the crystals positioned to reflect continuous beams of neutrons onto a common target. The various crystals are oriented to define increasingly large scattering angles throughout the row in order to increase the intensity of the Bragg reflected-diffracted beams. Such monochromators are incapable of distinguishing between elastically and inelastically scattered neutrons.
It is also known to use monochromators with multilayer mirrors as described by B. P. Schoenborn and D. L. Caspar (U.S. Pat. No. 3,885,153). Multilayered mirrors are resonant structures where the spacing of the layers is such that the multiple reflections from material interfaces add in phase or constructively interfere much in the same way as Bragg reflection-diffractions do from crystal planes as described above.
It is also known to use multi-channel xe2x80x9clensesxe2x80x9d monochromator described by S. W. Wilkins (U.S. Pat. No. 5,016,267). Multi-channel lenses are not rigorously lenses as they rely on reflection and not refraction, as common lenses do, for achieving focusing. They are formed by a number of channels where neutrons are directed by reflection to form a collimated beam or onto a xe2x80x9cfocalxe2x80x9d spot whose size is limited by the size of the channels of the device. They have been proposed for monochromatizing and collimating neutron beams but have not been adopted widely for such effects.
In accordance with preferred embodiments of the invention, a compound refractive lens for neutrons is provided having a plurality of individual unit Fresnel lenses comprising a total of N in number, the unit lenses hereinafter designated individually with numbers i=l through N. The unit lenses are aligned substantially aligned along an axis, the i-th lens having a displacement ti orthogonal to said axis, with the axis located such that             ∑              i        =        1            N        ⁢          xe2x80x83        ⁢          t      i        =  0.
Each of the unit lenses comprises a lens material having a refractive index decrement xcex4 less than 1 at a wavelength xcex less than 200 Angstroms. In a preferred mode, the neutron compound refractive lens above is configured such that the displacements ti are distributed such that there is a standard deviation "sgr"t of the displacements ti about the axis, wherein each of the unit lens has n zones, and wherein each of the unit lens has a smallest Fresnel zone width of snxe2x88x92snxe2x88x921, where sn and snxe2x88x921 are the zone radii of the n and nxe2x88x921 zones and the standard deviation is "sgr"txe2x89xa6[snxe2x88x92snxe2x88x921]/4.
a. Fresnel Lenses
The Fresnel configuration of the present invention shortens the length of the neutron compound refractive lens and increases the aperture of the lens while reducing the attenuation through it. This, in turn, increases the lens"" gain and collection efficiency. In addition, increasing the aperture size of the neutron lens increases the lens resolution when the compound neutron lens is used for imaging. The present invention also reduces diffuse scattering (mostly resulting in neutron energy change) of the neutrons passing through the lens thereby reducing overall background noise due to incoherently scattered neutrons.
b. Neutron Monochromator
In another embodiment a new type of monochromator is made by combining a neutron compound refractive lens with an aperture positioned at the image point of the lens. This increases the available neutron beam flux compared to those obtained from other types of neutron monochromators, as there is an increased gain from the use of a neutron refractive lens compared to reflection efficiencies and aperture optics used in the other instruments. The present invention provides for a simplified and inexpensive configuration of passive lenses. Also, the present invention provides for a dual-purpose instrument capable of collimating and monochromatizing neutron beams when used in the appropriate design configuration. In addition, the present invention provides differentiation between coherently focused neutrons and incoherently scattered ones. Further, the present invention provides steady-state high intensity neutron beams when used with a steady state source or pulsed high intensity neutron beams if either a pulsed neutron source is used, or if high repetition rate shutter is placed downstream from the neutron source or after the instrument.
c. Neutron Microscope
In a preferred embodiment, a neutron microscope is assembled (preferably for neutrons below 100 xc3x85 in wavelength) that includes a conventional source of neutrons, a neutron condensing optic that focuses neutrons on a specimen and, a neutron compound refractive lens that images with high resolution the specimen under investigation onto a neutron detector.
To illuminate specimens, use is made of conventional sources of neutrons such as nuclear reactors or spallation sources. One embodiment uses a condensing optic that maximizes the neutron flux delivered to the sample. The condensing optic may either be a reflective optic such as a curved neutron mirror or a neutron compound refractive lens. In an embodiment where a polychromatic source is used, a compound refractive lens condenser, in combination with a suitably placed diaphragm, monochromatizes the neutron beam and focuses on the specimen thereby maximizing the available neutron flux on the sample. In this embodiment the efficiency of the condenser illumination can be optimized with one optical element using xe2x80x9ccritical illuminationxe2x80x9d (as opposed to so called Kohler illumination that employs more than one optical element). xe2x80x9cCritical illuminationxe2x80x9d directly images the neutron source on the specimen.
In some embodiments the compound refractive lens that images the specimen onto the detector can be made to be achromatic. By doing so, this optic is the least affected by neutron beam bandwidth illuminating the specimen. Thus, the neutron compound refractive lens will produce high-resolution images of the specimen with no appreciable chromatic aberration from the neutron beam. The ability to make an achromatic compound refractive neutron lens is important so that relatively wide bandwidth neutron beams (typically between 1% and 10% bandwidths) can be used. Indeed, it is typically the case that these neutron CRLs should be made achromatic in order to achieve higher resolution. This can be done by properly spacing two compound refractive lenses.
Film or a neutron-sensitive two-dimensional detector can be used to observe the images of the specimen formed at the image plane. As one skilled in the art knows, there are other methods of recording the image.
In one embodiment the above conventional microscope that images objects in amplitude contrast can be converted into a microscope that images objects in phase contrast. In this manner, the present invention makes visible features in the specimen, which are not seen otherwise in amplitude contrast. This produces improved high-contrast images in regions of the specimen having low-amplitude-contrast surroundings. This embodiment produces phase-contrast images that will enhance research performed in biology, medicine, physical sciences and industry.
The conversion from an amplitude-contrast to a phase-contrast instrument is achieved by using either an annular condenser optic or an annular diaphragm on the condenser optic, such that the specimen is illuminated with an annular beam. A compound refractive lens then images this specimen with high resolution on to a neutron detector, which stores the image. A phase plate is placed in the rear focal plane of this compound refractive lens at the conjugate plane or at the transform plane of the annular condenser. The phase plate typically applies a 90xc2x0 or 270xc2x0 phase shift to the zero-order neutron rays coming from the specimen with respect to the rest of the neutron rays deflected by the sample. The thickness and material of the phase plate determine the phase shift introduced by the phase ring. A phase plate is placed in the conjugate or transform plane of the neutron objective where, if there were no diffraction from the specimen, the neutron rays would be focused to form an image of the condenser optic or annular diaphragm on the plate. On this phase plate there is a ring layer or a channel that matches the image of the condenser optic or annular diaphragm that introduces the 90xc2x0 or 270xc2x0 phase shift to the zero order neutron rays coming from the specimen.